UNIVERSITE LIBRE DE BRUXELLES
Laboratoire Transferts, Interfaces et Procédés (TIPS)
&
INSTITUT NATIONAL POLYTECHNIQUE
DE TOULOUSE
Interface, Institut de Mécanique des Fluides de Toulouse
Dynamics of bubbles in microchannels: theoretical, numerical and
experimental analysis
Thesis Submitted by
Omer Atasi
A thesis presented for the degree of Doctor of Philosophy
in
Engineering Science and Technology
Thesis advisors
:Benoît Haut, Université libre de Bruxelles
Dominique Legendre, Institut National Polytechnique de Toulouse
Benoit Scheid, Université libre de Bruxelles
Jury
:Anne De Wit, Université libre de Bruxelles
Frank Dubois, Université libre de Bruxelles
Benjamin Lalanne, Institut National Polytechnique de Toulouse
Emmanuelle Rio, Université Paris-Sud
ACKNOWLEDGEMENTS
Je remercie Frank Dubois d’avoir accepté de présider mon jury de thèse, Anne De Wit et Benjamin Lalanne d’avoir accepté de faire parti de ce jury et tout particulièrement Emmanuelle Rio et Stéphane Vincent pour avoir accepté d’être les rapporteurs de ma thèse.
Je tiens a remercier Benoît Haut et Benoit Scheid, mes promoteurs de thèse, en particulier. Outre le finance-ment de thèse FNRS que j’ai pu obtenir avec leur soutien, je leur suis reconnaissant de m’avoir soutenu pendant les périodes qui ont suivi les ruptures d’anévrisme que j’ai subies en 2013 et 2014. Concernant celà, je remercie également François Reniers, Laetitia Brone, et Anita Mathieu de l’Université libre de Bruxelles pour le soutien qu’ils m’ont apporté, tant financier que moral. De plus, je remercie tout particulièrement Benoît Haut d’avoir prolongé mon financement de thèse suite a l’année pendant laquelle je n’ai pas pu travailler.
Concernant mon apprentissage scientifique, je tiens à remercier mes promoteurs de thèse Benoît Haut, Benoit Scheid et Dominique Legendre, pour l’encadrement qu’ils m’ont fourni. En particulier, cette thèse a été l’occasion de m’initier à de nouveaux domaines et nouvelles techniques scientifiques, ce qui n’a été possible qu’avec leur patience et leur don à transmettre leurs connaissances. En particulier, je remercie Benoît Haut pour ses connais-sances et la rigueur qu’il m’a transmises durant cette thèse. Je remercie Dominique Legendre de m’avoir introduit dans le monde de la “Computational Fluid Dynamics", domaine où j’ai pu apprendre et m’épanouir. Je remercie tout particulièrement mon co-promoteur de thèse Benoit Scheid qui m’a offert l’unique occasion de séjourner pen-dant 8 mois à la Princeton University afin de travailler dans l’équipe du Professeur Howard A. Stone. Je remercie aussi le Prof. Howard Stone. J’ai pu apprécier sa dévotion à la science et au bien être de ses collaborateurs et sa disponibilité malgré son planning très chargé. Cette expérience m’a beaucoup apprise d’un point de vue sci-entifique et je lui en suis reconnaissant, ainsi qu’aux membres de son équipe, Sepideh Khodaparast, Estella Yu, Hyoungsoo Kim, Mirco Magnini et tous les autres.
Au sein de l’équipe du Laboratoire Transferts Interfaces et Procédés je tiens à remercier tout d’abord Sam Dehaeck, Adrien Dewandre et Alexei Rednikov pour leur contribution dans les aspects techniques de mon travail tant dans le domaine expérimental que théorique, et aussi Youen Vitry et Hervé Baudine de m’avoir assisté lors de problème technique au niveau des expériences conduites au laboratoire. Je remercie les membres et ex-membres du TIPs avec qui j’ai partagé de bons moments.
ABSTRACT
Keywords: microfluidics, bubbly flow, Taylor flow, surfactants, lubrication film
This thesis aims at contributing to the characterization of the dynamics of bubbles in microfluidics through model-ing and experiments. Two flow regimes encountered in microfluidics are studied, namely, the bubbly flow regime and the Taylor flow regime (or slug flow).
In particular, the first part of this thesis focuses on the dynamics of a bubbly flow inside a horizontal, cylindrical microchannel in the presence of surfactants using numerical simulations. A numerical method allowing to simulate the transport of surfactants along a moving and deforming interface and the Marangoni stresses created by an in-homogeneous distribution of these surfactants on this interface is implemented in the Level set module of the research code. The simulations performed with this code regarding the dynamics of a bubbly flow give insights into the complexity of the coupling of the different phenomena controlling the dynamics of the studied system. Fo example it shows that the confinement imposed by the microchannel walls results in a significantly different distribution of surfactants on the bubble surface, when compared to a bubble rising in a liquid of infinite extent. Indeed, surfactants accumulate on specific locations on the bubble surface, and create local Marangoni stresses, that drastically influence the dynamics of the bubble. In some cases, the presence of surfactants can even cause the bubble to burst, a mechanism that is rationalized through a normal stress balance at the back of the bubble. The numerical method implemented in this thesis is also used for a practical problem, regarding the artisanal production of Mezcal, an alcoholic beverage from Mexico.
The second part of the thesis deals with the dynamics of a Taylor flow regime, through experiments and analytical modeling. An experimental technique that allows to measure the thickness of the lubrication film forming between a pancake-like bubble and the microchannel wall is developed. The method requires only a single instantaneous bright-field image of a pancake-like bubble translating inside a microchannel. In addition to measuring the thickness of the lubrication film, the method also allows to measure the depth of a microchannel. Using the proposed method together with the measurment of the bubble velocity allows to infer the surface tension of the interface between the liquid and the gas. In the last chapter of this thesis, the effect of buoyancy on the dynamics of a Taylor flow is quantified. Though often neglected in microfluidics, it is shown that buoyancy effects can have a significant impact on the thickness of the lubrication film and consequently on the dynamics of the Taylor flow. These effects are quantified using experiments and analytical modeling. This work was performed at Princeton University with Professor Howard A. Stone during an eight month stay.
CHAPTER 1
Scientific Communications
1.1
Published articles
Atasi, O., Khodaparast, S., Scheid, B., Stone, H.A., 2017. Effect of buoyancy on the motion of long bubbles in horizontal tubes. Physical Review Fluids 2, 094304.
Khodaparast, S., Atasi, O., Deblais, A., Scheid, B., Stone, H.A., 2018. Dewetting of Thin Liquid Films Surround-ing Air Bubbles in Microchannels. Langmuir 34, 1363-1370.
Atasi, O., Haut ,B., Pedrono, A., Scheid, B., Legendre, D., 2018. Influence of soluble surfactants and deformation on the dynamics of centered bubbles in cylindrical microchannels. Langmuir 34, 10048-10062.
Atasi, O., Haut ,B., Dehaeck, S., Dewandre, A., Legendre, D., Scheid, B., 2018. How to measure the thickness of a lubrication film in a pancake bubble with a single snapshot ? Applied Physics Letter (Editor’s pick).
1.2
Submitted articles
G. Rage, Atasi, O., M. M. Wilhemus, J.F. Hernandez-Sanchez, Haut, B., Scheid, B., Legendre, D., Zenit, R., 2018. The pearls of mezcal: stability of surface bubbles as a traditional method to asses the ethanol content in distilled beverages . submitted to Proceedings of the National Academy of Science.
1.3
Scientific communications and conference papers
Atasi, O., Khodaparast, S., Scheid, B., Stone, H.A., 2016. Effect of gravity on the thin film surronding a bubble translating in a tube. American Physical Society, Division of Fluid Dynamics, 19-21 November, Portland, Oregon.
bubbles in water-alcohol mixtures with surfactants. American Physical Society, Division of Fluids Dynamics, 18-20 november, Denver, Colorado.
Atasi, O., Haut ,B., Scheid, B., Pedrono A., Legendre., D, Zenit., R., 2018. Numerical study of bubble bouncing and resting under a free surface in the presence of surfactants. Eurofoam, 9-12 July, Brussels, Belgium.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS 1 ABSTRACT 2 1 Scientific Communications 3 1.1 Published articles . . . 3 1.2 Submitted articles . . . 31.3 Scientific communications and conference papers . . . 3
2 Introduction 1 2.1 Bubbly flow and Taylor flow in microchannels . . . 1
2.2 Some important non dimensional numbers in microfluidics . . . 2
2.3 Use of surfactants in microfluidics . . . 3
2.4 Objectives of the thesis and structure of the manuscript . . . 3
I
Dynamics of bubbly flows in microchannels
5
3 Governing equations 6 3.1 Introduction . . . 63.2 Mass conservation . . . 6
3.3 Momentum conservation . . . 7
3.4 Surfactant mass conservation on the bubble surface . . . 7
3.4.1 The general form . . . 7
3.4.2 The normal time derivative form . . . 8
3.4.3 The Eulerian form . . . 9
4.2.1 One fluid formulation . . . 15
4.2.2 The projection method . . . 16
4.2.3 The Level-set method . . . 16
4.2.4 Spatial discretization . . . 17
4.2.5 Temporal discretization . . . 19
4.3 Numerical methodology to account for surfactants . . . 19
4.3.1 Transport of surfactants on the surface . . . 20
4.3.2 Transport of surfactants inside the bulk phase . . . 23
4.3.3 Marangoni stress . . . 23
4.4 Conclusion . . . 24
5 Validation of the numerical procedure 26 5.1 Validation of the numerical procedure used to transport surfactants on the bubble surface . . . . 26
5.1.1 Expansion test . . . 26
5.1.2 Advection test . . . 27
5.1.3 Adsorption/desorption test . . . 30
5.1.4 Diffusion test . . . 31
5.1.5 Discussion . . . 32
5.2 Exchange term in the surfactant tranport equation inside the bulk phase . . . 34
5.3 Marangoni stress . . . 36
5.4 Bubble rising in an infinite stagnant liquid . . . 37
5.5 Conclusion . . . 41
6 Influence of soluble surfactants and deformation on the dynamics of centered bubbles in cylindri-cal microchannels 42 6.1 Introduction . . . 42
6.2 Problem statement . . . 44
6.2.1 Geometry . . . 44
6.2.2 Equations and modeling assumptions . . . 44
6.2.3 Dimensional analysis . . . 46
6.3 Results . . . 46
6.3.1 Spherical bubbles . . . 47
6.3.2 Deformable bubble without surfactants . . . 50
6.3.3 Deformable bubble with surfactants . . . 54
6.4 Conclusion . . . 58 7 A numerical investigation of the lifetime of superficial bubbles inside Mezcal 60
7.1 Introduction . . . 60
7.2 Experimental observations . . . 62
7.3 Problem statement . . . 63
7.4 Setup for the simulations . . . 64
7.4.1 Domain . . . 64
7.4.2 Mesh . . . 64
7.5 Results . . . 66
7.5.1 Determination of the lifetime . . . 66
7.5.2 Role of surfactants . . . 67
7.5.3 Lifetime of bubbles as a function of the alcohol volume fraction. . . 69
7.5.4 Scaling analysis . . . 70
7.6 Conclusion and perspective . . . 73
II
Dynamics of Taylor flow in Microchannels
75
8 Introduction 76 8.1 Lubrication approximation . . . 768.2 The analysis of Bretherton . . . 77
8.3 Extension of the Bretherton model . . . 79
8.4 Conclusion . . . 80
9 How to measure the thickness of a lubrication film in a pancake bubble with a single snapshot? 81 9.1 Introduction . . . 81
9.2 Methodology . . . 84
9.2.1 Experimental setup . . . 84
9.2.2 Raytracing . . . 87
9.2.3 Model of the bubble shape . . . 88
9.3 Results and discussion . . . 91
10.2.1 Refractive index matching . . . 100
10.2.2 Experiments . . . 100
10.2.3 Visualization and image processing . . . 101
10.2.4 First experimental observation . . . 102
10.3 Theoretical predictions . . . 102
10.3.1 Thickness of the liquid film at the front of the bubble . . . 102
10.3.2 Inclination angle in the thin film region . . . 108
10.4 Experimental results and discussions . . . 108
10.4.1 Thickness of the liquid film at the front of the bubble . . . 108
10.4.2 Inclination of the bubble . . . 110
10.4.3 Liquid film at the back of the bubble . . . 111
10.5 Conclusion . . . 112
11 Conclusions and perspectives 114 11.1 Conclusion . . . 114
11.2 Perspectives . . . 116
12 Appendixes 118 12.1 Appendix A . . . 118
